The Most Predictive Physical Properties for the Stellar Population Radial Profiles of Nearby Galaxies
Guangwen Chen, Hong-Xin Zhang, Xu Kong, Zesen Lin, Zhixiong Liang, Xinkai Chen, Zuyi Chen, Zhiyuan Song
DDraft version May 15, 2020
Typeset using L A TEX twocolumn style in AASTeX63
The Most Predictive Physical Properties for the Stellar Population Radial Profiles of Nearby Galaxies
Guangwen Chen,
1, 2
Hong-Xin Zhang,
1, 2
Xu Kong,
1, 2
Zesen Lin,
1, 2
Zhixiong Liang,
1, 2
Xinkai Chen,
1, 2
Zuyi Chen,
1, 2 and Zhiyuan Song
1, 2 CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology ofChina, Hefei 230026, China School of Astronomy and Space Science, University of Science and Technology of China, Hefei 230026, China
Submitted to ApJABSTRACTWe present a study on the radial profiles of the D4000, luminosity-weighted stellar ages τ L , andluminosity-weighted stellar metallicities [ Z/ H] L of 3654 nearby galaxies (0 . < z < .
15) using theIFU spectroscopic data from the MaNGA survey available in the SDSS DR15, in an effort to explorethe connection between median stellar population radial gradients (i.e., ∇ D4000, ∇ τ L , ∇ [ Z/ H] L ) outto ∼ R e and various galaxy properties, including stellar mass ( M (cid:63) ), specific star formation rate(sSFR), morphologies, and local environment. We find that M (cid:63) is the single most predictive physicalproperty for ∇ D4000 and ∇ [ Z/ H] L . The most predictive properties for ∇ τ L are sSFR and, to a lesserdegree, M (cid:63) . The environmental parameters, including local galaxy overdensities and central–satellitedivision, have virtually no correlation with stellar population radial profiles for the whole sample,but the ∇ D4000 of star-forming satellite galaxies with M (cid:63) (cid:46) M (cid:12) exhibit a significant positivecorrelation with galaxy overdensities. Galaxies with lower sSFR have on average steeper negative stellarpopulation gradients, and this sSFR dependence is stronger for more massive star-forming galaxies.The negative correlation between the median stellar population gradients and M (cid:63) are best describedlargely as segmented relationships, whereby median gradients of galaxies with log M (cid:63) (cid:46) . M (cid:63) .While the dependence of the radial gradients of ages and metallicities on T-Types and central stellarmass surface densities are generally not significant, galaxies with later T-Types or lower central massdensities tend to have significantly lower D4000, younger τ L , and lower [ Z/ H] L across the radial rangesprobed in this study. Keywords: galaxies: evolution — galaxies: star formation — galaxies: general — galaxies: stellarcontent INTRODUCTIONThe stellar population distribution within galaxiesholds important clues to the assembly history of galax-ies. In the classical dissipative collapse models of galaxyformation (e.g., Eggen et al. 1962; Larson 1974; Carl-berg 1984; Pipino et al. 2010), the outer parts of galax-ies have less efficient star formation and self-enrichment
Corresponding authors: Hong-Xin Zhang, Xu [email protected]@[email protected] than the inner parts, due to lower gas densities and ashallower local potential well toward larger radii. In thisframework, galaxies naturally develop significant neg-ative abundance gradients and slightly positive stellarage gradients, with more massive galaxies having steepergradient slopes than lower mass galaxies. In the modernΛ cold dark matter (ΛCDM) paradigm of hierarchicalstructure formation, present-day galaxies have formedtheir central parts first, through either cold stream ac-cretion or violent disk instabilities (e.g., Dekel et al.2009) or galaxy merging, followed by a gradual buildupof galaxy disks from the inside out (e.g., Mo et al. 1998;Taylor & Kobayashi 2017), which gives rise to negative a r X i v : . [ a s t r o - ph . GA ] M a y Chen et al. radial gradients of both metallicities and stellar ages.Galaxy mergers are expected to play an important role(especially) at early cosmic epochs in the ΛCDM frame-work. Gas-poor mergers of comparable-mass galaxies(i.e., major mergers) can flatten preexisting stellar popu-lation gradients (Kobayashi 2004; Di Matteo et al. 2009),while gas-rich major mergers may preserve or regeneratenegative gradients (Bekki & Shioya 1999; Hopkins et al.2009).With the advent of large integral field unit (IFU)spectroscopic surveys in the past decade, such as theCalar Alto Large Integral Field Area (CALIFA; S´anchezet al. 2012), Sydney Australian Astronomical Observa-tory Multi-object Integral Field Spectrograph (SAMI;Bryant et al. 2015), and Mapping Nearby Galaxies atthe Apache Point Observatory (MaNGA; Bundy et al.2015), it has become possible to obtain the spatial dis-tribution of luminosity-weighted stellar ages and chem-ical abundances of large samples of galaxies in the localuniverse, which enables a direct investigation of the con-nection between stellar population gradients and othergalaxy properties and thus a relatively straightforwardtest of galaxy formation models in general.On one hand, the stellar population gradients are ex-pected to be affected by the internal properties of galax-ies. Studies of the radial profiles or gradients of the stel-lar ages and metallicities for over a hundred CALIFAgalaxies (e.g., P´erez et al. 2013; Gonz´alez Delgado et al.2014) revealed that the assembly of stellar mass andthe cessation of star formation proceed from the galac-tic centers to the outskirts for massive galaxies, in linewith the so-called “inside-out” growing mode, and thereseems to be a negative correlation between stellar pop-ulation gradients and stellar mass, which may naturallyconnect to the “outside-in” mode found for many nearbydwarf galaxies (Zhang et al. 2012). These findings agreewell with previous studies of the radial stellar gradi-ents based on multiwavelength broadband photometry(e.g., Tortora et al. 2010; Gonzalez-Perez et al. 2011;Pan et al. 2015, 2016). Recent studies found more com-plicated dependences of stellar population gradients onstellar mass or other properties based on larger samplesfrom the CALIFA survey (e.g., Garc´ıa-Benito, R. et al.2017; Gonz´alez Delgado et al. 2017) and the MaNGAsurvey (e.g., Ibarra-Medel et al. 2016; Goddard et al.2017a; Ellison et al. 2018; Wang et al. 2018b). In partic-ular, the radial gradients of metallicities were found todepend on morphologies (e.g., Hubble type) rather thanstellar mass in Gonz´alez Delgado et al. (2015). Woo &Ellison (2019) found that the radial gradients of stellarage, specific star formation rates (sSFR), and abundance(O/H) for isolated galaxies rely on the galaxy’s position on the diagram of stellar mass surface density within 1kpc (Σ ) and stellar mass. Based on a study of 62spiral galaxies, S´anchez-Bl´azquez et al. (2014) claimedthat there is no dependence of stellar population radialgradients on stellar mass or morphological types whengradients are normalized to the effective radius of galaxydisks.On the other hand, the environment of galaxies mightalso play a nonnegligible role in regulating the radialstellar population gradients. Schaefer et al. (2017) foundthat the SFR gradients are steeper in higher local galaxydensity based on 201 SFGs from the SAMI survey. How-ever, the radial gradients of stellar age and metallicityhave also been found to be independent of environmen-tal parameters (e.g., the large-scale structure type andthe local density in Zheng et al. 2017; the tidal strengthparameter and the central–satellite division in Goddardet al. 2017b).Above all, it is not clear whether and how differentgalaxy properties (either internal or external) affect theradial distribution of the stellar population in nearbygalaxies. In this work, taking advantage of IFU obser-vations of a large sample of nearby galaxies from themost recent data release of SDSS-IV MaNGA survey,we attempt to explore the connection of stellar popula-tion radial gradients with other galaxy properties suchas stellar mass, star formation, morphologies, and envi-ronments. Unlike most previous surveys that are eitherflux limited or volume limited, the MaNGA survey isdesigned to have a more or less uniform coverage in stel-lar mass. A series of recent studies have used the stel-lar population radial profiles of MaNGA galaxies to ex-plore the general topic of galaxy quenching (e.g., Li et al.2015; Goddard et al. 2017a; Belfiore et al. 2018; Wanget al. 2018b). The current paper focuses on a straight-forward question:
What physical properties are closelyconnected to the observed stellar population gradients ofnearby galaxies?
The outline of this paper is as follows. In Section 2,we describe our sample selection, determination of theradial gradients of D4000 indices, luminosity-weightedstellar ages, and luminosity-weighted stellar metallici-ties, as well as various morphological and environmentalproperties to be explored in this work. The results arepresented in Section 3, and the summary and discussionof our primary results follow in Section 4. DATA2.1.
Sample and Selection
As one of the three core programs in the fourth-generation Sloan Digital Sky Survey (SDSS-IV; Albaretiet al. 2017; Blanton et al. 2017), MaNGA (Bundyet al. 2015; Yan et al. 2016a,b) is an ongoing inte-gral field spectroscopic (IFS) survey for obtaining two-dimensional spectral mapping of ∼ . < z < . ∼ (cid:48)(cid:48) − (cid:48)(cid:48) onthe sky. The effective spatial resolution is 2 . (cid:48)(cid:48) α luminosities, andstellar mass for each galaxy. Because the Pipe3D SFRsand stellar masses are consistently estimated based onthe MaNGA data, we use their ratios to quantify thespecific sSFR for our galaxies. In addition, the NASASloan Atlas catalog (NSA; Blanton et al. 2011) providesauxiliary galaxy properties, such as the galaxy effectiveradius ( R e ), axis ratio ( b/a ), position angle, S´ersic in-dex ( n ) measured in the r band, and stellar masses forSDSS galaxies. The NSA stellar masses are determinedbased on the SDSS imaging data and are expected to bea better representation of the total stellar masses thanthose based on the MaNGA data. Throughout this pa-per, we use the NSA stellar masses M (cid:63) except when ex-ploring the mass–SFR relations (Figure 1a), where thePipe3D stellar masses (and SFR) are used. Because thePipe3D stellar parameters used in this work are based onthe Salpeter (1955) initial mass function (IMF), we ad-just the NSA stellar masses, which were originally basedon the Chabrier (2003) IMF, to be consistent with theSalpeter (1955) IMF.Following the quality control catalog included in thePipe3D VAC, 84 of the 4656 galaxies have either wrongredshift, poor signal-to-noise ratio (S/N), or other warn-ing issues and are thus excluded from our sample. These84 galaxies are excluded from our sample. In addition,532 galaxies that were observed with the 19-fiber IFUsare also excluded from our final sample because the ra-dial gradients estimated using the low spatial-resolutionIFUs may be subject to relatively large biases (e.g.,Ibarra-Medel et al. 2018). We also exclude 140 galaxiesthat have minor-to-major axis ratios ( b/a ) less than 0 . . < z < .
15, 10 M (cid:12) ≤ M (cid:63) ≤ M (cid:12) ,and 10 − M (cid:12) yr − < SFR < M (cid:12) yr − and aban-don galaxies without calculations of radial stellar popu-lation gradients (Section 2.2), which leaves us with 3654 galaxies in total. Both the “Primary” and “Secondary”MaNGA samples are used in this work.Figure 1a) shows the stellar mass–SFR distributionof our sample galaxies. We divide our sample intogalaxies above (MS+; 1132 galaxies) and below (MS − ;1222 galaxies) the galaxy star formation main sequence(SFMS) relation, and quiescent galaxies (QGs; 1300galaxies) by using the lines of demarcation from Cano-Daz et al. (2019).2.2. Radial stellar population gradients
Two-dimensional maps of the 4000˚A break (D4000)and stellar population parameters, including the surfacedensity of stellar mass, linear values of the luminosity-weighted stellar age ( τ L ), and logarithmic values of theluminosity-weighted stellar metallicity ([ Z/ H] L ), are re-trieved from Pipe3D pipeline. We choose to use theD4000 index as a representative age-sensitive observable,because this broad feature can be measured with rela-tively small uncertainties ( < δ line) atspectral S/Ns down to (cid:38) τ L and [ Z/ H] L from Pipe3D are derived through stel-lar population synthesis modeling of the MaNGA spec-tra, as described in S´anchez et al. (2016a,b). Pipe3Dalso produces mass-weighted stellar ages and metal-licities. Generally speaking, stellar population param-eters estimated from integrated spectra of unresolved(sub)galactic regions are biased toward younger stellarpopulations, and the constraints on older stellar popu-lations are unavoidably subject to larger uncertainties.On the other hand, the stellar mass contribution of rel-atively old stellar populations in local galaxies usuallydominates over that of young stellar populations. There-fore, the very poor constraints on star formation history(SFH) at ancient times means that the mass-weightedstellar parameters derived from integrated spectra aresubject to substantially larger uncertainties than theluminosity-weighted ones, which may frustrate any at-tempt to obtain useful estimates of mass-weighted pa-rameters for a comparative study as presented in thiswork. Throughout this paper, our discussion of stel-lar ages and metallicities is focused on the luminosity-weighted ones, but we also present the relevant resultsbased on mass-weighted ones in the Appendix (FiguresA1, A2, and A3). Chen et al. log
M [M fl ] l og S F R [ M fl y r − ] S F M S MS + + + + MS − − − − QGa) log
M [M fl ] l og Σ k p c [ M fl k p c − ] ↑ ∆ l o g Σ k p c > ↓ ∆ l o g Σ k p c < ↑ ∆ l o g Σ k p c > ↓ ∆ l o g Σ k p c < b) Figure 1: a) Distribution of our sample galaxies on the SFR– M (cid:63) plane. Star-forming galaxies and quiescent galaxiesare divided by the green dashed line (log SFR = 1 .
08 log M (cid:63) − . − ) the SFMS relation (blue dashed line; log SFR = 0 .
74 log M (cid:63) − .
64) adaptedfrom Cano-Daz et al. (2019). The purple contours enclose the central 25% − −
75% quantities of galaxies. b)Distribution of our sample on the Σ – M (cid:63) plane. The color scheme is as in the left panel. The solid black bentline is the best-fit Σ – M (cid:63) relation for our full sample (log Σ = 0 . M (cid:63) − .
95) + 9 .
44 for log M (cid:63) ≤ . = 0 . M (cid:63) − .
95) + 9 .
44 for log M (cid:63) > . ofgalaxies falling into individual 0.3 dex stellar mass bins.We derive the radial gradient slopes of the D4000, τ L ,and [ Z/ H] L of each galaxy by performing linear least-squares fitting to the median radial profiles. Specifically,we first calculate the deprojected galactocentric distanceof each spaxel by using the observed axis ratio of its hostgalaxy. Then, we obtain radial profiles of D4000, τ L and[ Z/ H] L by calculating the median D4000, τ L and [ Z/ H] L of spaxels falling within the 2 . (cid:48)(cid:48) ∇ D4000 = d D4000 d ( R/R e ) , (1) ∇ τ L = dτ L [Gyr] d ( R/R e ) , (2) ∇ [ Z/ H] L = d [ Z/ H] L d ( R/R e ) , (3)where R/R e is the radius in units of the effective radius.A negative ∇ D4000 represents a larger D4000 in thegalactic center compared to its outskirts, correspond-ing to the inside-out scenario, while a positive ∇ D4000is consistent with the outside-in scenario. We note thatonly spaxels with S/N ≥ ≥ ≥ ∼ R e , we only analyze theirradial profiles out to ∼ R e in order to be consistentwith the “Primary” sample.It is worth noting that we choose to quantify the gra-dients of ages on linear scales instead of the logarithmicscales that were adopted in many previous studies. Thesame linear age gradient corresponds to flatter logarith-mic age gradients at older ages than at younger ages,which may give one a misleading impression that stellarage gradients flatten over time. Indeed, we found thatthe logarithmic age gradients become significantly flat-ter for galaxies with lower sSFR (not shown here), butthe linear age gradients barely show such a trend (Figure3). 2.3. Morphological Properties
In order to quantify the morphological dependenceof stellar population radial profiles of our galaxies, weconsider four morphological parameters, i.e., T-Type,stellar mass surface density averaged within the central1 kpc (Σ ), central velocity dispersion ( σ cen ), andS´ersic index n (S´ersic 1968). The T-Type values are re-trieved from the MaNGA PyMorph Photometric andDeep Learning Morphological Catalogs (Fischer et al.2019). Σ is calculated by summing up the stellarmass map within the central 1 kpc of each galaxy. σ cen is retrieved from the Pipe3D VAC (S´anchez et al. 2018),and the S´ersic index n is retrieved from the NSA catalog(Blanton et al. 2011).The T-Type values of our sample galaxies are quanti-fied as T = − . × P (Ell) − . × P (S0) + 2 . × P (Sab) +6 . × P (Scd) (Meert et al. 2015), where P is the proba-bility of the morphological class indicated in parentheses(Huertas-Company et al. 2011). This T-Type definitionhas been extensively used to quantify the visual mor-phologies of galaxies (e.g., Nair & Abraham 2010; Wil-lett et al. 2013; Domnguez Snchez et al. 2018). Accordingto this definition, elliptical and S0 galaxies (ETG) haveT-Types ≤
0, while late-type disk galaxies (LTG) haveT-Types > has been widely used to quantify the cen-tral stellar mass surface densities (Fang et al. 2013;Wang et al. 2018a; Woo & Ellison 2019). There isa well-established correlation between Σ and M (cid:63) (e.g., Figure 1b). We perform piecewise linear least-squares fitting to log Σ as a function of log M (cid:63) for our galaxies. The best-fit broken linear relation islog Σ = 0 . M (cid:63) − .
95) + 9 .
44 for log M (cid:63) ≤ .
95, log Σ = 0 . M (cid:63) − .
95) + 9 .
44 forlog M (cid:63) > .
95. In what follows, we use the vertical off-set of log Σ (∆ log Σ ) with respect to this best-fit log Σ –log M (cid:63) relation to quantify the relative ex-cess or deficit of the central stellar mass of each galaxyfor its M (cid:63) . We note that, at given stellar masses, the∆ log Σ difference is more or less equivalent to thelogarithmic difference of the bulge-to-total mass ratios( B/T ). 2.4.
Environmental Parameters
In order to explore the environmental dependence ofstellar population radial profiles, we separate our sam-ple into central and satellite galaxies by using the halo-based group catalog of SDSS galaxies derived by Limet al. (2017), and then use the projected local galaxyoverdensity within a projected distance to the fifth near-est neighbor to quantify the local environment of eachgalaxy. The Lim et al. (2017) group catalog improvesupon that of Yang et al. (2005, 2007) and Lu et al.(2016), with a more uniform group halo assignment overa wider range of halo masses M halo . The local overdensi-ties are quantified as log(1+ δ ) = log (1 + ( ρ i − ρ m ) /ρ m )(Etherington & Thomas 2015), where ρ i is the localgalaxy number density and ρ m is the mean galaxy num-ber density. Among our sample galaxies, 2569 havelog(1 + δ ) measurements available in the Galaxy En- vironment for MaNGA Value Added Catalog (GEMA-VAC, Argudo-Ferndez et al. in prep.), and among these2569 galaxies, 2543 have available central–satellite divi-sion (1699 centrals and 844 satellites). RESULTSThis section is devoted to an exploration of the con-nection of the radial profiles of D4000, τ L and [ Z/ H] L with the various galaxy properties introduced above. Wefirst present an evaluation of the relative importance ofdifferent galaxy properties in predicting ∇ D4000, ∇ τ L ,and ∇ [ Z/ H] L , as well as the average D4000, τ L , and[ Z/ H] L within 0.5 effective radius (i.e., D4000 cen , τ L , cen and [ Z/ H] L , cen ) and around one effective radius (i.e.,D4000 R e , τ L , R e and [ Z/ H] L , R e ), of our sample galaxiesusing a Random Forests (RF; Breiman 2001) algorithm,and then present the dependence of stellar populationprofiles on the most relevant galaxy properties sepa-rately.3.1. The Most Predictive Properties for StellarPopulation Profiles
We adopt the RF estimator implemented in thePython package scikit-learn (Pedregosa et al. 2011)to evaluate the relative importance of different galaxyproperties in predicting ∇ D4000, ∇ τ L , and ∇ [ Z/ H] L ,as well as D4000 cen , τ L , cen , [ Z/ H] L , cen , D4000 R e , τ L , R e ,and [ Z/ H] L , R e . The RF algorithm is an ensemble methodcommonly used in astrophysics not only for classification(e.g., Dubath et al. 2011; Richards et al. 2011), but alsoin regression (e.g., Miller et al. 2015), where the pre-diction can be for a real-valued response variable. Moredetails of the decision tree regression can be found inHastie et al. (2009) and Kuhn & Johnson (2013). Ba-sically, the RF estimator fits a number of decision treeclassifiers on various subsamples randomly drawn withreplacement from our galaxy sample and uses the av-eraging of individual decision trees to improve the pre-dictive accuracy. Every decision tree in the ensemble istrained by using a random selection of features (i.e., thegalaxy properties we are interested in) to split galaxysamples belonging to the tree. The more often a featureis used in splitting galaxies of a tree, the more importantthat feature is, and the final relative importance of thedifferent galaxy properties in predicting our stellar pop-ulation parameters of interest is simply the average offeature importances of individual trees in the ensemble.Because a fraction of our galaxies do not have log(1 + δ ) measurements, we run the RF estimator separatelyon the full sample to evaluate the relative impor-tance of M (cid:63) , sSFR, T-Type, ∆ log Σ , σ cen , andS´ersic index n , and on the subsample of 2569 galaxies Chen et al. R e l a t i v e I m p o r t a n c e f o r ∇ D ( % )
88 77 55
99 66 55 66 R = 0 . for all galaxies in sample R = 0 . for galaxies with log(1 + δ ) R e l a t i v e i m p o r t a n c e f o r D ( % )
11 11
00 0044
33 11 88 11 00 R = 0 . for D4000 cen R = 0 . for D4000 Re R e l a t i v e I m p o r t a n c e f o r ∇ τ L ( % )
55 44
77 55 66 R = 0 . for all galaxies in sample R = 0 . for galaxies with log(1 + δ ) R e l a t i v e i m p o r t a n c e f o r τ L [ G y r ] ( % )
11 33
00 0044
22 22
00 00 R = 0 . for τ L , cen R = 0 . for τ L , Re logM logsSFR T - Type ∆logΣ σ cen S´ersic n log(1 + δ ) R e l a t i v e I m p o r t a n c e f o r ∇ [ Z / H ] L ( % )
99 88 99 99 66
77 88 77 55 77 R = 0 . for all galaxies in sample R = 0 . for galaxies with log(1 + δ ) logM logsSFR T - Type ∆logΣ σ cen S´ersic n log(1 + δ ) R e l a t i v e i m p o r t a n c e f o r [ Z / H ] L ( % )
33 22
11 1188
77 44
33 33 R = 0 . for [Z / H] L , cen R = 0 . for [Z / H] L , Re Figure 2:
Left column: evaluation of the relative importance of different galaxy properties in predicting the radialgradients ∇ D4000 (top), ∇ τ L (middle), and ∇ [ Z/ H] L (bottom) of our galaxies by using the RF estimator. The graybars in each panel represent results for the whole sample, and the white bars represent results for the subsamplewith log(1 + δ ) measurements. Right column: evaluation of the relative importance of different galaxy properties inpredicting D4000, τ L , and [ Z/ H] L at the galaxy center (purple bars) and one effective radius (orange bars) of oursample galaxies with log(1 + δ ) measurements. The coefficient of determination R returned from each RF run isindicated in each panel. See the text for more details.with log(1 + δ ) measurements for the relative impor-tance of M (cid:63) , sSFR, T-Type, ∆ log Σ , σ cen , n andlog(1 + δ ). The most important parameters for settingup the RF estimator are the number of decision trees(n estimators) and the minimum number/fraction ofsamples for node splitting (min samples split). The min-imum number/fraction of samples at a splitted leaf node(min samples leaf) is set to be min samples split/2. Af-ter extensive testing, we find that the final results do not change with n estimators as long as n estimators ≥ −
10% of the number of our galaxies). Lastly, wemention that the two criteria for measuring the qualityof tree splitting “MSE” and “MAE” supported in the RFestimator give nearly the same results for our samples,and we choose to use the “MSE” criterion for presentingour results.Figure 2 presents the RF ranking results by usingn estimator = 1000 and min samples split = 1%. Theleft column shows the results for radial gradients, whilethe right column shows the results for average stellarpopulation parameters at the galaxy center and nearone effective radius, respectively. For the sake of clarity,only subsamples with local overdensity measurementsare considered for the average stellar population param-eters. The coefficient of determination R for each RFrun, which quantifies the fraction of variance of the datathat is “explained” by the model, is indicated in Figure2. R normally ranges from 0.0 to 1.0 (best), but may gonegative when the model is arbitrarily worse. The rela-tive feature importance for a given RF run is normalizedsuch that the sum for all the explored properties is equalto one.3.1.1. Ranking of galaxy properties for radial gradients
For radial gradients, it is obvious that M (cid:63) is the mostpredictive property for ∇ D4000 (top-left panel of Fig-ure 2), and the next two most predictive properties for ∇ D4000 are, in order of decreasing importance, sSFRand T-Type. The first three most predictive propertiescombined account for ∼
80% of the total feature impor-tances. It is noteworthy that local galaxy overdensitieshave a very weak correlation with ∇ D4000. We also ex-plored the importance of being central or satellite galax-ies (not shown here) and found that the central-satellitedivision has almost zero predictive power for ∇ D4000.D4000 varies with both stellar ages and metallicities.The middle and bottom panels of the left column of Fig-ure 2 show the RF ranking results for ∇ τ L and ∇ [ Z/ H] L ,respectively. sSFR and, to a lesser degree, M (cid:63) are thetwo most predictive properties for ∇ τ L , while M (cid:63) is thesingle most predictive property for ∇ [ Z/ H] L . Therefore,the apparent dependence of ∇ D4000 on M (cid:63) is primarilya metallicity effect, while the apparent dependence of ∇ D4000 on sSFR is primarily an age effect.3.1.2.
Ranking of galaxy properties for stellar populationsat center and one effective radius
As is shown in the right column of Figure 2, the sSFRis the single most predictive property for D4000 and τ L at both the galaxy center and one effective radius forour sample. As the second most predictive property forlocal D4000 and τ L , the central velocity dispersion σ cen has a significantly smaller predictive power than sSFR.For central [ Z/ H] L , M (cid:63) is the most predictive property. However, at one effective radius, sSFR is the single mostpredictive property for [ Z/ H] L , similar to D4000 and τ L .3.2. Dependence of Stellar Population Gradients onStellar Mass and sSFR
The whole sample is split into three stellar mass bins:9 ≤ log M (cid:63) ≤
10 (low-mass galaxies), 10 < log M (cid:63) ≤ < log M (cid:63) ≤ ∇ D4000 (top row), ∇ τ L (middle row), and ∇ [ Z/ H] L (bottom row) with integrated sSFR for galaxies in thethree stellar mass bins (from the first to the thirdcolumns). In each panel, MS+, MS − , and QGs areplotted with blue, green, and red symbols, respectively.Smoothing curves of the 25% − − ∇ D4000, ∇ τ L , and ∇ [ Z/ H] L along thesSFR axis are calculated by using the ComprehensiveR Archive Network (CRAN) package Constrained B-Splines (COBS; Ng & Maechler 2007, 2020), which givesqualitatively constrained smoothing spline curves. Todetermine the uncertainties of the median curves, werandomly resample with replacement the original sam-ple for 1000 times and perform the spline quantile re-gression to each realization.For the intermediate- and high-mass bins, the median ∇ D4000 gradually varies from nearly zero to increas-ingly more negative values as sSFR decreases, reachesthe minimum at ∼ . − (cid:38) ∇ D4000of the low-mass galaxies stays close to zero until sSFRfalls > ∇ D4000 values at a given sSFR are smaller (i.e., morenegative) for more massive galaxies. The median ∇ τ L exhibits a similar variation with sSFR at given M (cid:63) , inline with the RF ranking results that the sSFR depen-dence of ∇ D4000 is primarily driven by stellar age ef-fect (Section 3.1). The median ∇ [ Z/ H] L becomes morenegative as sSFR decreases for the intermediate-massgalaxies but stays more or less constant for the low- andhigh-mass galaxies.Figure 4 further illustrates a continuous mass-dependent variation of the median ∇ D4000, ∇ τ L ,and ∇ [ Z/ H] L for the MS+, MS − , and QG sub-samples. Smoothing curves depicting the 25% − −
75% quantities of the galaxy distribu-tions as well as the uncertainties of the medians fordifferent subsamples are calculated in the same way asin Figure 3. The mass-dependent variations for star-forming galaxies generally follow much shallower slopes
Chen et al. − . − . − . . . ∇ D4000 − − − − − − − l og s S F R [ y r − ] M [M fl ] 10 (787) MS +MS +MS − MS − QGQG − . − . − . . . ∇ D4000 < logM [M fl ] 11 (1551) MS +MS +MS − MS − QGQG − . − . − . . . . ∇ D4000 < logM [M fl ] 12 (1316) MS +MS +MS − MS − QGQG − − − ∇ τ L − − − − − − − l og s S F R [ y r − ] MS +MS +MS − MS − QGQG − − − ∇ τ L MS +MS +MS − MS − QGQG − − − ∇ τ L MS +MS +MS − MS − QGQG − . − . . . ∇ [Z / H] L − − − − − − − l og s S F R [ y r − ] MS +MS +MS − MS − QGQG − . − . . . ∇ [Z / H] L MS +MS +MS − MS − QGQG − . − . . . ∇ [Z / H] L MS +MS +MS − MS − QGQG
Figure 3:
Global sSFR is plotted against stellar population gradients (from top to bottom: ∇ D4000, ∇ τ L , and ∇ [ Z/ H] L ) for galaxies in different log M (cid:63) bins, as indicated at the top of each column. In each panel, the thick solidcurve represents the median trend, and the dark shaded region marks the uncertainties of the median trend. The lightshaded regions are bounded by the smoothed curves of the 25% −
75% quantiles of the galaxy distribution. Both themedian and 25% −
75% quantiles are determined with the nonlinear spline quantile regression method. The uncertaintiesof the median trend are determined based on the random resampling of the original sample with replacement 1000times. The two dashed horizontal lines divide the sample into MS+ (blue dots), MS − (green dots), and QG (red dots)subsamples. The number of galaxies in each stellar mass bin is given in parentheses at the top of the correspondingcolumn.at log M (cid:63) (cid:46) . − .
5, above which the MS − subsampleexhibits significantly steeper slopes than the MS+ sub-sample for ∇ D4000 and ∇ τ L . It is noteworthy that whilethe median ∇ [ Z/ H] L monotonically decreases with M (cid:63) across the whole mass range, the median ∇ τ L of MS − galaxies reaches the most negative values at log M (cid:63) ∼ ρ to measure the correlation between stellar pop-ulation gradients and stellar mass for each subsample.We also determine the standard deviation of ρ based onrandom resampling of the original samples with replace-ment. As indicated in Figure 4, there exist significantcorrelations ( ρ > .
2) between the explored radial gra- . . . log M [M fl ] − . − . − . . . . ∇ D ρ = − . ± . ρ = − . ± . ρ = − . ± . ρ = − . ± . ρ = − . ± . ρ = − . ± . . . . log M [M fl ] − − − ∇ τ L ρ = − . ± . ρ = − . ± . ρ = − . ± . ρ = − . ± . ρ = − . ± . ρ = − . ± . . . . log M [M fl ] − . − . . . ∇ [ Z / H ] L ρ = − . ± . ρ = − . ± . ρ = − . ± . ρ = − . ± . ρ = − . ± . ρ = − . ± . Figure 4:
Stellar population gradients (from left to right: ∇ D4000, ∇ τ L , and ∇ [ Z/ H] L ) as a function of stellarmasses for MS+ (blue), MS − (green), and QG (red). As in Figure 3, the thick solid curves in each panel representthe median trend for different subsamples, and the dark shaded regions mark the uncertainties of the median trend.The light shaded regions mark the smoothed 25% −
75% quantiles of the galaxy distribution. Both the median and25% −
75% quantiles are determined with the nonlinear spline quantile regression method. The Spearman’s rankingcorrelation coefficients ρ for different galaxy samples and their standard deviations determined based on 1000 MonteCarlo realizations are indicated in each panel.dients and stellar masses, except for the ∇ τ L of the QGsubsample.3.3. Dependence of Stellar Population Profiles onGalaxy Morphologies
We have shown that stellar mass and sSFR are thetwo parameters that have the strongest correlation withstellar population gradients in previous sections. Herewe explore the secondary dependence of stellar popu-lation gradients on morphological properties, as quan-tified by T-Type and ∆ log Σ , by controlling thestellar mass and sSFR. The dependence of the median ∇ D4000, ∇ τ L , and ∇ [ Z/ H] L on T-Type and ∆ log Σ for MS+, MS − , and QGs in the three stellar mass binsdefined in Section 3.2 are presented in Figures 5 and 7.The smoothing curves of the 25% − − ρ > . τ L ,and [ Z/ H] L with T-Type and ∆ log Σ , we divide oursamples into separate bins of T-Type ( ≤ >
0) and∆ log Σ ( > ≤ separately. 3.3.1. Dependence on T-Type
As is shown in Figure 5, galaxies of higher stellarmasses generally have more negative median ∇ D4000, ∇ τ L , and ∇ [ Z/ H] L at given T-Type and sSFR ranges.The median ∇ D4000 and ∇ τ L are generally more nega-tive at later T-Types for given mass and sSFR ranges.However, we point out that the overall negative corre-lation between ∇ τ L and T-Types are not significant forall but the intermediate-mass MS+ and high-mass MS − subsamples. There is no significant correlation betweenT-Types and ∇ [ Z/ H] L for any subsamples. Neverthe-less, the median D4000, τ L and [ Z/ H] L of earlier-type(smaller T-Types) galaxies are generally larger than thatof later-type (larger T-Types) galaxies across the probedradial ranges for any given mass and sSFR ranges (Fig-ure 6).The overall more significant negative correlation be-tween ∇ D4000 and T-Types than that between ∇ τ L and T-Types may be qualitatively explained by the factthat the derivative of D4000 with respect to age de-creases with age for a passively evolving stellar popu-lation. The same stellar age radial gradient results ina shallower D4000 radial gradient for earlier T-Types,which tend to have overall older ages. We can concludehere that the morphological type is a property that isconnected with galaxy stellar populations largely in aradius-independent way.3.3.2. Dependence on ∆ log Σ
As with T-Types, galaxies of higher stellar massesgenerally have more negative median ∇ D4000, ∇ τ L and0 Chen et al. ∇ D . fl ] 10 . ρ = 0 . ± . ρ = − . ± . ρ = − . ± . . < logM [M fl ] 11 . ρ = 0 . ± . ρ = − . ± . ρ = − . ± . . < logM [M fl ] 12 . ρ = − . ± . ρ = − . ± . ρ = − . ± . ∇ τ L ρ = 0 . ± . ρ = − . ± . ρ = − . ± . ρ = 0 . ± . ρ = − . ± . ρ = − . ± . ρ = − . ± . ρ = − . ± . ρ = − . ± . T - Type ∇ [ Z / H ] L ρ = 0 . ± . ρ = − . ± . ρ = 0 . ± . T - Type ρ = 0 . ± . ρ = 0 . ± . ρ = 0 . ± . T - Type ρ = − . ± . ρ = − . ± . ρ = − . ± . Figure 5:
Dependence of stellar population gradients on T-Types. Results for ∇ D4000, ∇ τ L , and ∇ [ Z/ H] L areshown respectively in the top , middle , and bottom rows. Galaxies that fall in the low (9 ≤ log M (cid:63) ≤ < log M (cid:63) ≤
11) and high (11 < log M (cid:63) ≤
12) stellar mass ranges are plotted, respectively, in the left , middle , and right columns. In each panel, MS+, MS − , and QGs are plotted with blue, green and red colors, respectively. The25% − −
75% quantities of the subsample galaxies with 1 σ uncertainties of the median smoothing curveand the Spearman correlation coefficients ρ with uncertainties for the subsamples are calculated in the same way asFigure 4. Note that the existence of a correlation is only confirmed for ρ > . ∇ [ Z/ H] L at given ∆ log Σ and sSFR ranges. Whilethe dependence of ∇ D4000 on ∆ log Σ is generallynot significant except for the low- and intermediate-mass MS+ subsamples, the median trend is generallyin the opposite sense with that on T-Types (Figure 7),which probably reflects the expected negative correla-tion between T-Types and central mass concentrationsin general. Particularly, the ∇ D4000 of the low- andintermediate-mass MS+ subsamples exhibit significantpositive correlations with ∆ log Σ , and the median ∇ D4000 becomes positive at the high ∆ log Σ end.Such positive dependence on ∆ log Σ is also found for the median ∇ τ L . Therefore, the low- and intermediate-mass MS+ galaxies with higher ∆ log Σ tend to havemore centrally concentrated star formation activities.The correlation between ∇ [ Z/ H] L and ∆ log Σ isgenerally very weak. Although the dependence of ra-dial gradients on ∆ log Σ is overall weak, galaxieswith higher ∆ log Σ have on average larger D4000,older τ L and higher [ Z/ H] L than those with smaller∆ log Σ across the probed radial ranges for any givenmass and sSFR ranges (Figure 8), which suggests that,similar to T-Types, central stellar mass concentration is1 N . fl ] 10 . T - Type > : T - Type > : | T - Type 0 : T - Type 0 : | T - Type > : T - Type > : | T - Type 0 : T - Type 0 : | T - Type > : T - Type > : | T - Type 0 : T - Type 0 : | . < logM [M fl ] 11 . T - Type > : T - Type > : | T - Type 0 : T - Type 0 : | T - Type > : T - Type > : | T - Type 0 : T - Type 0 : | T - Type > : T - Type > : | T - Type 0 : T - Type 0 : | . < logM [M fl ] 12 . T - Type > : T - Type > : | T - Type 0 : T - Type 0 : | T - Type > : T - Type > : | T - Type 0 : T - Type 0 : | T - Type > : T - Type > : | T - Type 0 : T - Type 0 : | D τ L [ G y r ] R [ R e ] [ Z / H ] L R [ R e ] R [ R e ] Figure 6:
Median coadded radial profiles of D4000, τ L , and [ Z/ H] L for early-type galaxies (ETGs: T-Type ≤ >
0; open symbols). The solid and dashed lines in each panelrepresent linear least-squares fitting to ETGs and LTGs, respectively. Division of the samples into different ranges ofstellar mass and sSFR, and the color coding scheme are as in Figure 5. Median coadded radial profiles are plotted onlywhen there are more than 15 data points in a given bin. The number of galaxies in different subsamples is also listedat the top of each column.a property that is connected with galaxy stellar popula-tions largely in a radius-independent way.3.4.
Dependence of Stellar Population Profiles onEnvironments
As in Section 3.3, we also explored the dependence ofthe median ∇ D4000, ∇ τ L and ∇ [ Z/ H] L on local galaxyoverdensities log(1 + δ ) for both central and satellitesubsamples, but did not find significant correlations forall but the low-mass star-forming satellite galaxies whichexhibit positive correlations between ∇ D4000 and localoverdensities ( ρ > ∼ .
2) and may indicate a suppression of star formation at larger radii by tidal disturbances ofnearby galaxies. The corresponding plots are not shownhere for clarity. The median coadded radial profiles forcentral and satellite galaxies with log(1 + δ ) > ≤ . δ ) environment have slightly (albeit systemically) largerD4000, older τ L and higher [ Z/ H] L than those locatedin lower log(1 + δ ) environment across the probed radialranges. Therefore, the local environment has influenceon galaxy stellar populations in a global sense for all2 Chen et al. ∇ D . fl ] 10 . ρ = − . ± . ρ = 0 . ± . ρ = 0 . ± . . < logM [M fl ] 11 . ρ = − . ± . ρ = 0 . ± . ρ = 0 . ± . . < logM [M fl ] 12 . ρ = 0 . ± . ρ = − . ± . ρ = 0 . ± . ∇ τ L ρ = − . ± . ρ = 0 . ± . ρ = 0 . ± . ρ = − . ± . ρ = − . ± . ρ = 0 . ± . ρ = − . ± . ρ = − . ± . ρ = − . ± . ∆logΣ [M fl kpc − ] ∇ [ Z / H ] L ρ = − . ± . ρ = 0 . ± . ρ = 0 . ± . ∆logΣ [M fl kpc − ] ρ = − . ± . ρ = − . ± . ρ = 0 . ± . ∆logΣ [M fl kpc − ] ρ = − . ± . ρ = 0 . ± . ρ = − . ± . Figure 7:
Same as Figure 5, but for the dependence of radial gradients of D4000, τ L , and [ Z/ H] L on ∆ log Σ .star-forming galaxies, and also in a local sense for low-mass star-forming galaxies. SUMMARY AND DISCUSSION4.1.
Summary of major results from this work
Based on IFU spectroscopic data of a large sam-ple of 3654 nearby galaxies with 10 M (cid:12) ≤ M (cid:63) ≤ M (cid:12) from the MaNGA survey available in theSDSS DR15, we have explored the dependence of ra-dial profiles of stellar populations, as quantified bythe nearly extinction-free observable D4000, and themodel-dependent luminosity-weighted stellar ages τ L ,and luminosity-weighted stellar metallicities [ Z/ H] L , onvarious galaxy properties. We find that M (cid:63) is the mostpredictive global physical property for the D4000 radialgradients ∇ D4000, and the next most predictive prop-erties for ∇ D4000, in order of decreasing importance,are sSFR, T-Type, and ∆ log Σ . The strongest pre-dictive power of M (cid:63) on ∇ D4000 reflects the strongest predictive power of M (cid:63) on the metallicity gradient ∇ [ Z/ H] L . The first and second most predictive proper-ties for the age gradient ∇ τ L are sSFR and M (cid:63) , respec-tively. The local environment quantified by the galaxyoverdensities log(1+ δ ) have overall very weak predictivepower for radial gradients of the whole sample, but star-forming satellite galaxies with M (cid:63) (cid:46) M (cid:12) exhibita positive correlation between ∇ D4000 and log(1 + δ ),which may imply a significant suppression of star for-mation activities of relatively low-mass galaxies at largeradii by tidal disturbances of nearby galaxies.Regarding local stellar population values, the sSFRand, to a much lesser degree, the central velocity disper-sion are the most predictive global properties for D4000and τ L values at both the galaxy center and effectiveradius for our sample. For local [ Z/ H] L , M (cid:63) is the mostpredictive property at the galaxy center, while sSFRis the single most predictive property at one effectiveradius. The environmental properties, as quantified by3 N . fl ] 10 . ∆logΣ : ∆logΣ : | ∆logΣ > : ∆logΣ > : | ∆logΣ : ∆logΣ : | ∆logΣ > : ∆logΣ > : | ∆logΣ : ∆logΣ : | ∆logΣ > : ∆logΣ > : | . < logM [M fl ] 11 . ∆logΣ : ∆logΣ : | ∆logΣ > : ∆logΣ > : | ∆logΣ : ∆logΣ : | ∆logΣ > : ∆logΣ > : | ∆logΣ : ∆logΣ : | ∆logΣ > : ∆logΣ > : | . < logM [M fl ] 12 . ∆logΣ : ∆logΣ : | ∆logΣ > : ∆logΣ > : | ∆logΣ : ∆logΣ : | ∆logΣ > : ∆logΣ > : | ∆logΣ : ∆logΣ : | ∆logΣ > : ∆logΣ > : | D τ L [ G y r ] R [ R e ] [ Z / H ] L R [ R e ] R [ R e ] Figure 8:
Same as Figure 6, but for the median coadded radial profiles of D4000, τ L , and [ Z/ H] L for galaxies withcompact cores (∆ log Σ >
0; filled symbols) and diffuse cores (∆ log Σ ≤
0; open symbols).log(1 + δ ) and the central-satellite division, have virtu-ally no correlation with galaxy stellar populations forthe whole sample, but star-forming galaxies located ina higher log(1 + δ ) environment have on average largerD4000, older τ L , and higher [ Z/ H] L across the probedradial ranges, without regard for being central or satel-lite.The correlation of stellar population gradients with M (cid:63) and sSFR is in the sense that galaxies with higher M (cid:63) or lower sSFR tend to have steeper negative gradi-ents. Moreover, the negative correlation of median stel-lar population gradients with M (cid:63) at a given sSFR is bestdescribed by segmented relationships, whereby galaxieswith log M (cid:63) (cid:46) − . M (cid:63) . Galaxies with a higher global sSFR or younger age generally also havehigher sSFR or younger ages locally at given galacto-centric distances. The morphological properties (e.g., T-Type, Σ ) are connected with galaxy stellar popula-tions largely in a radius-independent way.4.2. Comparison to relevant results in the literature
Our finding that the sSFR and, to a much lesser de-gree, the central velocity dispersion are the most predic-tive properties for local stellar ages within galaxies is inline with a recent study by Bluck et al. (2019). In partic-ular, Bluck et al. (2019) found that the offset from thegalaxy SFMS and, to a lesser degree, the central velocitydispersion of host galaxies are the two most predictiveparameters for whether or not a spatially resolved regionis quenched. Here we further show that sSFR is also the4
Chen et al. N . fl ] 10 . log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | (a) Central Galaxies . < logM [M fl ] 11 . log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | . < logM [M fl ] 12 . log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | . fl ] 10 . log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | (b) Satellite Galaxies . < logM [M fl ] 11 . log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | . < logM [M fl ] 12 . log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | log(1+ δ ) 0 . : log(1+ δ ) 0 . : | log(1+ δ ) > . : log(1+ δ ) > . : | D τ L [ G y r ] R [ R e ] [ Z / H ] L R [ R e ] R [ R e ] R [ R e ] R [ R e ] R [ R e ] Figure 9:
Same as Figure 6, but for the median coadded radial profiles of the D4000, τ L , and [ Z/ H] L of the (a) centralgalaxies and (b) satellite galaxies located in environments with different local overdensities.single most predictive global property for [ Z/ H] L at oneeffective radius, but at the galaxy center, stellar mass isthe most important property for predicting [ Z/ H] L .The positive correlation between stellar age gradi-ents and the sSFR of star-forming galaxies suggeststhat (1) quenching of star formation proceeds spatiallyfrom inside out on average, and this inside-out trendis more significant for more massive galaxies, and (2)the star formation boost with respect to the SFMS pri-marily happens in the inner parts of galaxies, result-ing in flatter or even positive stellar population gra-dients at higher sSFR. To the best of our knowledge,previous spectroscopic studies of the radial gradientsof nearby galaxies mostly focus on the dependence onmorphological types and mass (e.g., S´anchez-Bl´azquezet al. 2014; Gonz´alez Delgado et al. 2015; Zheng et al.2017), but rarely explore the dependence on the globalstar formation status of galaxies, which turns out tobe the most predictive property for stellar age gradi-ents. Gonz´alez Delgado et al. (2015) claimed that it isthe Hubble type, rather than stellar mass, that has theclosest connection to stellar age gradients, based on 300CALIFA galaxies. They also found that age/metallicitygradient slopes reach a minimum (i.e., the most nega-tive value) in Sb-Sbc galaxies and increase toward eitherearlier or later Hubble types. With an order of magni- tude larger sample, we have shown that the sSFR and,to a lesser degree, stellar masses, rather than Hubbletypes (here quantified by T-Types) are the most predic-tive properties for stellar age gradients. At a given sSFRand stellar masses, the radial gradient slopes appear tomonotonically decrease with T-Types, without an up-turn at any intermediate T-Type values. Moreover, evenat the same Hubble types, stellar age gradients generallyexhibit a positive dependence on sSFR for given stellarmasses (Figure 5).The close connection between stellar age gradients andsSFR reported here is also in line with Ellison et al.(2018), who studied the radial star formation profilesof galaxies available in the MaNGA DR13 and foundthat the relative excess or deficit of star formation as afunction of radius is correlated with the vertical offset ofgalaxies with respect to the global SFMS. Our analysissuggests that this close connection still exists when di-viding galaxies into different stellar masses. In addition,Pan et al. (2016) studied the radial variations of thebroadband (NUV − r ) color of ∼ M (cid:63) < . − r ) vari-5ations should be primarily attributed to a metallicityeffect, rather than an age effect. Wang et al. (2018b)used the mass-weighted fraction of quenched spaxelswith D n (4000) > α ) < n (4000), EW(H δ A ), and EW(H α ), whereas the TQgalaxies have much weaker average gradients than star-forming and PQ galaxies over the whole stellar massranges. This is inconsistent with our finding that stel-lar population gradients generally become more nega-tive as sSFR decreases, except at log M (cid:63) (cid:38) .
5, whereQGs have radial gradients of D4000 and τ L that areshallower than those of MS − galaxies but steeper thanthose of MS+ galaxies. The difference may be primarilyattributed to a difference in the star formation statusclassification schemes adopted in our work and Wanget al. (2018b). The classification of the global star for-mation status of a galaxy should be based on the globallyintegrated sSFR, regardless of the relative spatial distri-butions of young and old stellar populations. D n (4000)and EW(H α ) maps reflect the proportional, instead ofabsolute, contribution of younger or poorer-metal stel-lar populations in any spaxels, which means that spax-els with the same amount of young stellar populationsmay be classified by Wang et al. (2018b) as being star-forming if located in the outer low stellar density regions(or galaxies with lower stellar masses and thus generallylower surface mass densities) or quenched if located inthe inner high stellar density regions (or galaxies withhigher stellar masses and thus higher surface mass den-sities). It is thus conceivable that there is some mass-dependent overlap in global sSFRs between the star-forming and PQ subsamples as well as between the PQand TQ subsamples in Wang et al. (2018b), which tendsto smear out the sSFR or mass dependence of stellarpopulation radial gradients.By using local stellar mass densities, galactocentricdistances (in kiloparsecs) and host galaxy stellar massesas control parameters, Woo & Ellison (2019) obtainedaverage radial profiles of relative enhancement (or off-set) of sSFR (or ages) for the relatively isolated galax-ies with either compact (∆ log Σ >
0) or diffusecores (∆ log Σ < > < R e -normalized(rather than using physical units of kiloparsecs) radialprofile stacking separately for galaxies with differentstellar masses and sSFR, we do not observe substan-tially larger ∆ log Σ -dependent differences betweenthe median D4000/ages at smaller galactocentric dis-tances than at larger galactocentric distances, regard-less of the current sSFRs (Figure 8). Moreover, star-forming galaxies with compact cores tend to have simi-lar or higher central stellar metallicities than those withrelatively diffuse cores.Our finding of a lack of significant correlation betweenstellar population gradients and local galaxy overden-sities is largely in line with previous studies based onMaNGA data (Goddard et al. 2017b; Zheng et al. 2017;Spindler et al. 2018). Nevertheless, we additionally showthat this lack of correlation applies to both star-formingand quiescent galaxies, which implies that local over-densities do not significantly affect the stellar popula-tion distribution in galaxies over either short or longtimescales.4.3. Implications for a Negative Dependence of StellarPopulation Gradients on Stellar Mass
The classical monolithic dissipative collapse modelsof galaxy formation (e.g., Larson 1974; Carlberg 1984;Pipino et al. 2010) are qualitatively consistent with ourfinding of a monolithic negative dependence of stellarmetallicity gradients on stellar mass, but are incon-sistent with the overall negative stellar age gradients.In the ΛCDM hierarchical structure formation mod-els, galaxy mergers are expected to be common espe-cially in the early universe (e.g., Duncan et al. 2019).The early gas-dominated merging events (along withaccretion-driven violent disk instabilities; e.g., Dekel &Burkert 2014) might have formed the central parts of thepresent-day galaxies first, and later, the fallback of rel-atively high angular momentum cold gas ejected duringthe merging process might have rebuilt extended disksfrom inside out (e.g., Barnes 2002), giving rise to neg-ative radial gradients of stellar ages and metallicities.Some numerical simulations (e.g., Bekki & Shioya 1999;Hopkins et al. 2009) suggest that gas-rich major mergersinvolving more massive progenitors give rise to steepermetallicity gradients due to a stronger central starburstsustained by tidally induced gas inflow.Nevertheless, more recent simulations by Taylor &Kobayashi (2017) suggest that gas-rich major mergersdo not significantly steepen metallicity gradients when6
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44 22
22 22
22 22 R = 0 . for τ M , cen R = 0 . for τ M , Re logM logsSFR T - Type ∆logΣ σ cen S´ersic n log(1 + δ ) R e l a t i v e I m p o r t a n c e f o r ∇ [ Z / H ] M ( % )
44 88 77 44 44
55 88 88 44 33 44 R = 0 . for all galaxies in sample R = 0 . for galaxies with log(1 + δ ) logM logsSFR T - Type ∆logΣ σ cen S´ersic n log(1 + δ ) R e l a t i v e I m p o r t a n c e f o r [ Z / H ] M ( % )
99 88 22
11 11
66 44
33 44 R = 0 . for [Z / H] M , cen R = 0 . for [Z / H] M , Re Figure A1:
Same as Figure 2, but for the evaluation of the relative importance of different galaxy properties inpredicting the radial gradients of mass-weighted ages and metallicities ( ∇ τ M and ∇ [ Z/ H] M ), and mass-weighted ages τ M and metallicities [ Z/ H] M at galaxy centers (purple bars) and R e (orange bars).0 Chen et al. − − − ∇ τ M − − − − − − − l og s S F R [ y r − ] M [M fl ] 10 (787) MS +MS +MS − MS − QGQG − − − ∇ τ M < logM [M fl ] 11 (1551) MS +MS +MS − MS − QGQG − − − ∇ τ M < logM [M fl ] 12 (1316) MS +MS +MS − MS − QGQG − . − . . . ∇ [Z / H] M − − − − − − − l og s S F R [ y r − ] MS +MS +MS − MS − QGQG − . − . . . ∇ [Z / H] M MS +MS +MS − MS − QGQG − . − . . . ∇ [Z / H] M MS +MS +MS − MS − QGQG
Figure A2:
Same as Figure 3, but for global sSFR plotted against mass-weighted stellar population gradients ( ∇ τ M and ∇ [ Z/ H] M ) for galaxies in different log M (cid:63) bins. . . . log M [M fl ] − − − ∇ τ M ρ = − . ± . ρ = − . ± . ρ = − . ± . . . . log M [M fl ] − . − . . . ∇ [ Z / H ] M ρ = − . ± . ρ = − . ± . ρ = − . ± . Figure A3:
Same as Figure 4, but for mass-weighted stellar age and metallicity gradients (from left to right: ∇ τ M and ∇ [ Z/ H] M ) as a function of stellar masses for MS+ (blue), MS −−